Definition 1 ([1]}, [2]}) 
In the Stable Roommate Problem (SR) \(n\)  agents rank every other agent in a strict order of preference. They must be paired in such a way that there are no blocking pairs (see Definition REF ). If we allow agents' preference lists to be incomplete, the problem is called Stable Roommate Problem with Incomplete Lists (SRI). If agent \(a_i\) 's preference list contains another agent \(a_j\) , we say \(a_i\)  finds \(a_j\)  acceptable, otherwise \(a_i\)  finds \(a_j\)  unacceptable.

